Heart transplantation has become in recent decades an established method for the treatment of advanced heart failure. Precisely, it was in January 2014 when 30 years have passed since the start of clinical heart transplantation program at the Institute for Clinical and Experimental Medicine. 936 heart transplants were performed by the end of 2013. The transplant program has reached considerable development since its beginnings. The knowledge of whole issue has deepened, indication criteria have been extended, new immunosuppressives are available and many of them are still in research. Life expectancy of patients has been prolonged and quality of life has improved. Nevertheless, the care of transplant patient is very complicated task for medical professionals and brings a lot of problems to solve.